A275997 Numbers k whose deficiency is 64: 2k - sigma(k) = 64.

134, 284, 410, 632, 1292, 1628, 4064, 9752, 12224, 22712, 66992, 72944, 403988, 556544, 2161664, 2330528, 8517632, 13228352, 14563832, 15422912, 20732792, 89472632, 134733824, 150511232, 283551872, 537903104, 731670272, 915473696, 1846850576, 2149548032, 2159587616

Offset

1,1

Comments

Any term x = a(m) in this sequence can be used with any term y in A275996 to satisfy the property (sigma(x)+sigma(y))/(x+y) = 2, which is a necessary (but not sufficient) condition for two numbers to be amicable.

The smallest amicable pair is (220, 284) = (A275996(2), a(2)) = (A063990(1), A063990(2)), where 284 - 220 = 64 is the abundance of 220 and the deficiency of 284.

The amicable pair (66928, 66992) = (A275996(7), a(11)) = (A063990(18), A063990(19)), where 66992 - 66928 = 64 is the deficiency of 66992 and the abundance of 66928.

Links

Table of n, a(n) for n=1..31.

Example

a(1) = 134, since 2*134 - sigma(134) = 268 - 204 = 64.

Mathematica

Select[Range[10^7], 2 # - DivisorSigma[1, #] == 64 &] (* Michael De Vlieger, Jan 10 2017 *)

Prog

(PARI) isok(n) = 2*n - sigma(n) == 64; \\ Michel Marcus, Dec 30 2016

Crossrefs

Cf. A002025, A063990, A275996.

Sequence in context: A050963 A051387 A177348 * A370162 A007251 A219443

Adjacent sequences: A275994 A275995 A275996 * A275998 A275999 A276000

Keyword

nonn

Author

Timothy L. Tiffin, Aug 16 2016

Extensions

More terms from Jinyuan Wang, Mar 02 2020

Status

approved